Download or read book Generalizations of the M bius Inversion Formula written by Ellen R. Fisher and published by . This book was released on 1969 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Generalizations of the M bius Inversion Formula written by Doris Ann Gentry and published by . This book was released on 1964 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Incidence Algebras written by Eugene Spiegel and published by Routledge. This book was released on 2022-01-26 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work covers the maximal and prime ideals of the incidence algebra, derivations and isomorphisms, radicals and additional ring-theoretic properties. Combinatorial discussions include a study of the Mobius function, reduced incidence subalgebras, and the coalgebra approach to incidence algebras.
Download or read book Mobius Inversion In Physics written by Nanxian Chen and published by World Scientific. This book was released on 2010-04-28 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book attempts to bridge the gap between the principles of pure mathematics and the applications in physical science. After the Möbius inversion formula had been considered as purely academic, or beyond what was useful in the physics community for more than 150 years, the apparently obscure result in classical mathematics suddenly appears to be connected to a variety of important inverse problems in physical science.This book only requires readers to have some background in elementary calculus and general physics, and the prerequisite knowledge of number theory is not needed. It will be attractive to our multidisciplinary readers interested in the Möbius technique, which is a tiny but important part of the number-theoretic methods. It will inspire many students and researchers in both physics and mathematics. In a practical problem, continuity and discreteness are often correlated, and few textbooks have given attention to this wide and important field as this one.Clearly, this book will be an essential supplement for many existing courses such as mathematical physics, elementary number theory and discrete mathematics.
Download or read book Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2017-08-10 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.
Download or read book Classical Theory of Arithmetic Functions written by R Sivaramakrishnan and published by Routledge. This book was released on 2018-10-03 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on the classical theory of number-theoretic functions emphasizing algebraic and multiplicative techniques. It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs. The author is head of the Dept. of Mathemati
Download or read book Handbook of Number Theory I written by József Sándor and published by Springer Science & Business Media. This book was released on 2005-11-17 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.
Download or read book Handbook of Number Theory II written by J. Sándor and published by Springer Science & Business Media. This book was released on 2004 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.
Download or read book A Theory of Generalized Donaldson Thomas Invariants written by Dominic D. Joyce and published by American Mathematical Soc.. This book was released on 2011 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.
Download or read book Introduction to Arithmetical Functions written by Paul J. McCarthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty years, attests to its popularity. Most textbooks on the theory of numbers contain some information on arithmetical functions, usually results which are classical. My purpose is to carry the reader beyond the point at which the textbooks abandon the subject. In each chapter there are some results which can be described as contemporary, and in some chapters this is true of almost all the material. This is an introduction to the subject, not a treatise. It should not be expected that it covers every topic in the theory of arithmetical functions. The bibliography is a list of papers related to the topics that are covered, and it is at least a good approximation to a complete list within the limits I have set for myself. In the case of some of the topics omitted from or slighted in the book, I cite expository papers on those topics.
Download or read book Parameterized Algorithms written by Marek Cygan and published by Springer. This book was released on 2015-07-20 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.
Download or read book Certain Number Theoretic Episodes In Algebra Second Edition written by R Sivaramakrishnan and published by CRC Press. This book was released on 2019-03-19 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
Download or read book Bijective Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2011-02-10 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical
Download or read book Number Theory written by Benjamin Fine and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Analytic number theory and algebraic number theory both receive a solid introductory treatment. The book’s user-friendly style, historical context, and wide range of exercises make it ideal for self study and classroom use.
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 1228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Analysis of Evolution Information and Complexity written by Wolfgang Arendt and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.
Download or read book Handbook of Topological Fixed Point Theory written by Robert F. Brown and published by Springer Science & Business Media. This book was released on 2005-07-21 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
